Browsing by Author "Guo, Jong-Shenq"

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DEAD-CORE AT TIME INFINITY FOR A HEAT EQUATION WITH STRONG ABSORPTION
(2009-08-01)
Fu, Sheng-Chen
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Guo, Jong-Shenq
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Wu, Chin-Chin
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應用數學系
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Department of Applied Mathematics
We study an initial boundary value problem for a heat equation with strong absorption. We first prove that the solution of this problem stays positive for any finite time and converges to the unique steady state for a large class of initial data. This gives an example in which the dead-core is developed in infinite time. Then some estimates of the dead-core rate(s) are derived. Finally, we provide the uniformly exponential rate of convergence of the solution to the unique steady state.
THE SIGN OF TRAVELING WAVE SPEED IN BISTABLE DYNAMICS
(2020-06-01)
Guo, Jong-Shenq
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Nakamura, Ken-Ichi
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Ogiwara, Toshiko
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Wu, Chang-Hong
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應用數學系
We are concerned with the sign of traveling wave speed in bistable dynamics. This question is related to which species wins the competition in multiple species competition models. It is well-known that the wave speed is unique for traveling wave connecting two stable states. In this paper, we first review some known results on the sign of wave speed in bistable two species competition models. Then we derive rigorously the sign of bistable wave speed for a special three species competition model describing the competition in two different circumstances: (1) two species are weak competitors and one species is a strong competitor; (2) three species are very strong competitors. It is interesting to observe that, under certain conditions on the parameters, two weaker competitors can wipe out the strongest competitor.